Prepare the frequency table of scores on the upper face of
the die and find the mean score.

Solution:

Number on the upper face of die

Number of times it occurs (frequency)

fixi

1

2

1 × 2 = 2

2

2

2 × 2 = 4

3

5

3 × 5 = 15

4

1

4 × 1 = 4

5

4

5 × 4 = 20

6

6

6 × 6 = 36

Therefore, mean of the data = ∑(fixi)/∑fi

= (2 + 4 + 15 + 4 + 20 + 36)/20

= 81/20

= 4.05

3. If the mean of the following distribution is 9, find the value of p.

X

4

6

p + 7

10

15

f

5

10

10

7

8

Solution:

Calculation of mean

xi

fi

xifi

4

5

20

6

10

60

p + 7

10

10(p + 7)

10

7

70

15

8

120

∑fi = 5 + 10 + 10 + 7 + 8 = 40

∑ fixi = 270 + 10(p + 7)

Mean = ∑(fixi)/∑fi

9 = {270 + 10(p + 7)}/40

⇒ 270 + 10p + 70 = 9 × 40

⇒ 340 +10p = 360

⇒ 10p = 360 - 340

⇒ 10p = 20

⇒ p = 20/10

⇒ p = 2

Mean of grouped data:

While calculating the mean of the grouped data, the values x1, x2, x3, ……. xn are taken as the mid-values or the class marks of various class intervals. If the frequency distribution is inclusive, then it should be first converted to exclusive distribution.

4. The following table shows the number of plants in 20 houses in a group